Su Wan Park , Nak Hoon Bark , Kwan Woo Ryu

The KIPS Transactions:PartA, Vol. 16, No. 6, pp. 419-426, Dec. 2009
10.3745/KIPSTA.2009.16.6.419,   PDF Download:

Abstract

To realistically simulate fluid, the Navier-Stokes equations are generally used. Solving these Navier-Stokes equations on the Eulerian framework, the non-linear advection terms invoke heavy computation and thus Semi-Lagrangian methods are used as an approximated way of solving them. In the Semi-Lagrangian methods, the locations of advection sources are traced and the physical values at the traced locations are interpolated. In the case of Stam’s method, there are relatively many chances of numerical losses, and thus there have been efforts to correct these numerical errors. In most cases, they have focused on the numerical interpolation processes, even simultaneously using particle-based methods. In this paper, we propose a new approach to reduce the numerical losses, through improving the tracing method during the advection calculations, without any modifications on the Eulerian framework itself. In our method, we trace the grids with the velocities which will let themselves to be moved to the current target position, differently from the previous approaches, where velocities of the current target positions are used. From the intuitive point of view, we adopted the simple physical observation: the physical quantities at a specific position will be moved to the new location due to the current velocity. Our method shows reasonable reduction on the numerical losses during the smoke simulations, finally to achieve real-time processing even with enhanced realities.

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